Polynomial identities, indices, and duality for theN=1 superconformal modelSM(2, 4v)

We prove polynomial identities for theN=1 superconformal modelSM(2, 4v) which generalize and extend the known Fermi/Bose character identities. Our proof uses theq-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq-series on the fermionic side. We use these polynomials to demonstrate a dual relation underq→q−1 betweenSM(2, 4v) andM(2v−1, 4v). We also introduce a genralization of the Witten index which is expressible in terms of the Rogers false theta functions.

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